Yes, obviously if you think about it logically it doesn't make sense, but if anyone here has ever taken any level of calculus, you'd know that it is mathematically true. Please don't dispute me just because you haven't learned it yet.

starting at 1
1 divided by 2 = 1/2
1/2 divided by 2 = 1/4
1/4 divided by 2 (now going to be a comma for the pleasure of the reader) = 1/8
1/8, = 1/16
1/16, = 1/32
1/32, = 1/64, however the distance the frog is from the wall, will never reach 0 :)

There may be no measurement we know of that can measure something smaller than the planck length, however, it does not mean we do not have the means to discover it :) so according to current sciences, yes the frog can reach the wall. But that's the good thing about science, is that it's constantly changing.

that's the beautiful thing about it. science used to say the frog shouldn't reach the wall, but of course he does! the idea is that once 2 things get down to the plank length within each other, it's by all means impossible to distinguish between the atoms of the two objects. there essences literally intercede and become one. the frog;s atoms and the walls intermingle, and they "touch."

Now back to serious mode, that's why I said CURRENT SCIENCES. We do not truly know anything in this world, because there will always be someone there to prove you wrong. We say the planck length is the smallest measurement, but that's only the smallest measurement that we can see, if we were able to 'zoom in' on that object even more, we would see an even smaller measurement take place.
Think of it as two stars. If we can only observe them at a certain distance, it may seem as though they are right next to each other, or touching, and that's all that our current distance system can give us. In forty years or so, Johnny Pearpit can come along and invent a device that allows you to view things 300x closer than what we saw before, and now we realize that they are not in fact touching, but they are so close they look as if they're touching :).

Hahahh, thanks for the applause. But you're right quantum theory stands to be disproved. That's physical sciences for ya.

But the mathematical solution to the paradox allows for the frog to take an infinite amount of steps in a finite amount of time. which is really cool, and proven. both by rigorous mathematical proof, and of course, by demonstration.

The frog would never hop to the wall by hopping halfway.
But, eventually, it would be impossible for him to hop halfway: He would overshoot it.
If you can give me a link to this proof, I will gladly read it.
Gweetie's link was a wiki page about geometric series in general, not the frog problem

there are a couple of solutions on this page, though i could show you the short proof that it takes a finite amount of time to take the infinite amount of steps which does indeed involve the geometric series.

Again, I couldn't find, on the page, this particular problem.
I tried ctrl + f and searched for frog, found nothing.
Also searched for half and found a few things, but nothing relating to this problem in particular.

True, Homer does reach the locomotive in the second scenario...
But Homer isn't attempting to go half the distance with each step.
Eventually, one step will step over the remaining distance, regardless of how small or large.
He wouldn't be traveling half the distance anymore.
This is like saying that Pi has a definite end because circles are closed.

He reaches it in both cases.
and well pi definitely is a finite number, no question about it.
but take it like this:
say the frog is traveling at a speed v, and starts out at a distance d from the wall.
then the time (d/2)*v + (d/4)*v + (d/8)*v + ... = (vd)*(the infinite sum of the reciprocals of powers of 2)
vd is finite.
the infinite sum of the reciprocal of powers of 2 is finite.
if ab=c and both a and b are finite, then c must also be finite.
which means that t is finite.
the frog can and does reach the wall.
and both physics and mathematics back that up.

Ok... I just spent a while trying to come up with a response, but deleted it realizing that it made no sense.
The only thing I can come up with to say is that, as a word problem, it makes no sense that the frog would touch the wall.
Maybe if the amount of time was infinite, i don't know.
I quit.
My brain hurts...
You win.